So my problem is this: "A non-negative function f has the property that its ordinate set over an arbitrary interval has an area proportional to the arc length of the graph above the interval. Find f"
So i started with the integral of f and the definition of arc length in 2-space integral ( sqrt(1 + f ' (x)^2)) and then set them equal to each other. but then i get this:
f(x) ^ 2 = 1 + f ' (x) ^ 2
But I don't know how to solve this. Any help will be great.